The time-dependent motion of flexural waves generated by the vibration of an elastic plate resting on a variable Winkler foundation with compression is studied. The physical problem is analysed under the assumption of small amplitude structural response in two dimensions. The dispersion equation is analysed in detail, and points of wave blocking are shown to exist. The time-dependent propagation is simulated for the case of both constant and variable properties. For the case of varying properties, it is shown that the wave amplitude near the blocking point for this class of flexural waves satisfies the hyper-Airy differential equation, which is solved analytically in terms of the fourth-order Airy function. Further, the asymptotic solution of the hyper-Airy differential equation is derived by employing the WKB method to match the far-field solution with the near-field solution. The results obtained analytically are compared with a novel time-domain simulation based on a spectral method.

研究了由弹性板的振动产生的弯曲波的时间相关运动，该板位于可变温克勒基础上并受压。物理问题在二维小幅结构响应假设下进行分析。详细分析了色散方程，表明存在阻波点。对于恒定和可变属性的情况，模拟了与时间相关的传播。对于性质不同的情况，表明该类弯曲波在阻塞点附近的波幅满足超艾里微分方程，该方程根据四阶艾里函数进行解析求解。更多，采用WKB方法将远场解与近场解相匹配，推导出超艾里微分方程的渐近解。将分析获得的结果与基于频谱方法的新型时域模拟进行比较。